Computing derivative-based global sensitivity measures using polynomial chaos expansions

TL;DR

This paper demonstrates how polynomial chaos expansions can be used to efficiently compute derivative-based global sensitivity measures, reducing computational costs in sensitivity analysis of complex models.

Contribution

It introduces a method to analytically compute DGSMs using PCE, enabling faster sensitivity analysis especially for high-dimensional models.

Findings

Efficient computation of DGSMs via PCE demonstrated on benchmark problems.

Analytical derivatives of orthonormal polynomials facilitate post-processing.

Method reduces computational effort compared to traditional variance-based methods.

Abstract

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The {\em derivative-based global sensitivity measures} (DGSM) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis.